Question

f(x) = tan(x) ^ arctan(x)

Find f'(x).

Answer 1

\[f(x) = (\tan x)^{\arctan x}\]

Answer 2

believe the only function that acts as its own inverse (i.e. f^-1(x) = f(x)) is y = x.

Answer 3

did i help at all?

Answer 4

not really, the answer in the back of the book is ridiculously long

Answer 5

http://gyazo.com/83c8c62b3f1098672c155d554aee7da2

Answer 6

u have to take logarithm of both sides and then u get ln(f(x))=arctan(x)ln(tanx)
is it f'(x)= tan(x) ^ arctan(x)((ln(tanx)/(1+x^2)) + (arctanx)((sec^2x)/(tanx))))
=tan(x) ^ arctan(x)( ln(tanx)/(1+x^2) + (arctanx)(secx)(cosecx) )

Answer 7

The final answer anded up being \[f'(x) = tanx ^{arctanx}\left( \frac{ lntanx }{ 1+x^2 } + arctanxcotxsec^2x\right)\]
Thanks!

Answer 8

welcome i hope u understand that (arctanx)(secx)(cosecx) =(arctanx)(sec^2x)(cotx)